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A245299 Decimal expansion of the Landau-Kolmogorov constant C(5,4) for derivatives in the case L_infinity(-infinity, infinity).

%I A245299 #9 Feb 16 2025 08:33:23
%S A245299 1,4,9,6,2,7,7,8,6,9,7,3,8,8,4,4,7,3,8,5,0,8,1,0,2,1,3,9,3,2,9,7,8,2,
%T A245299 5,5,3,3,1,7,0,0,6,2,4,7,0,9,3,2,5,4,1,0,3,0,8,7,5,6,8,6,3,9,5,0,3,6,
%U A245299 8,0,0,9,7,2,0,4,5,0,0,4,3,3,7,4,5,7,0,3,5,8,1,0,9,0,8,3,9,6,3,9,6,9,2,0,9
%N A245299 Decimal expansion of the Landau-Kolmogorov constant C(5,4) for derivatives in the case L_infinity(-infinity, infinity).
%C A245299 See A245198.
%D A245299 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 3.3 Landau-Kolmogorov constants, p. 213.
%H A245299 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/Landau-KolmogorovConstants.html">Landau-Kolmogorov Constants</a>
%H A245299 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/FavardConstants.html">Favard Constants</a>
%F A245299 C(n,k) = a(n-k)*a(n)^(-1+k/n), where a(n) = (4/Pi)*sum_{j=0..infinity}((-1)^j/(2j+1))^(n+1) or a(n) = 4*Pi^n*f(n+1), f(n) being the n-th Favard constant A050970(n)/A050971(n).
%F A245299 C(5,4) = (15/2)^(1/5).
%e A245299 1.49627786973884473850810213932978255331700624709325410308756863950368...
%t A245299 a[n_] := (4/Pi)*Sum[((-1)^j/(2*j+1))^(n+1), {j, 0, Infinity}]; c[n_, k_] := a[n-k]*a[n]^(-1+k/n); RealDigits[c[5,4], 10, 105] // First
%Y A245299 Cf. A050970, A050971, A244091, A245198.
%K A245299 nonn,cons,easy
%O A245299 1,2
%A A245299 _Jean-François Alcover_, Jul 17 2014